Related papers: Dilations of non-Markovian dynamical systems on gr…

We consider contractive homomorphisms of a planar algebra ${\mathcal A}(\Omega)$ over a finitely connected bounded domain $\Omega \subseteq \C$ and ask if they are necessarily completely contractive. We show that a homomorphism…

In this paper, we consider the decomposition of multigraphs under minimum degree constraints and give a unified generalization of several results by various researchers. Let $G$ be a multigraph in which no quadrilaterals share edges with…

For a complex Banach space $\mathbb X$, we prove that $\mathbb X$ is a Hilbert space if and only if every strict contraction $T$ on $\mathbb X$ dilates to an isometry if and only if for every strict contraction $T$ on $\mathbb X$ the…

We introduce the scaling function associated to a graph directed Markov system, and show that it is a H\"{o}lder continuous function of the dual symbolic Cantor set. With some natural separation and regularity conditions, each such system…

Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, we explore a pure algebraic…

For nonuniform exponentially bounded evolution families defined on Banach spaces, we introduce a class of Banach function spaces, whose norms are completely determined by the nonuniform behaviour of the corresponding evolution family. We…

We consider a continuous family of linear elliptic differential operators of arbitrary order over a smooth compact manifold with boundary. Assuming constant dimension of the spaces of inner solutions, we prove that the orthogonalized…

We extend a contraction mapping argument for ordinary state-dependent delay differential equations to evolutionary partial differential equations in the sense of R. Picard, that is, to equations of the form $\bigl(\partial_{t}…

We continue the study dilation of linear maps on vector spaces introduced by Bhat, De, and Rakshit. This notion is a variant of vector space dilation introduced by Han, Larson, Liu, and Liu. We derive vector space versions of Wold…

The notion of nonpositive curvature in Alexandrov's sense is extended to include p-uniformly convex Banach spaces. Infinite dimensional manifolds of semi-negative curvature with a p-uniformly convex tangent norm fall in this class on…

We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…

We present a completely new structure theoretic approach to the dilation theory of linear operators. Our main result is the following theorem: if $X$ is a super-reflexive Banach space and $T$ is contained in the weakly closed convex hull of…

The classical global linearization theorem for autonomous system given in [C. Pugh, Amer. J. Math., 91 (1969) 363-367] requires that nonlinear system with hyperbolicity satisfies boundedness and Lipschitz continuity.In this paper, we…

We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph…

Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…

We present a spectral mapping theorem for continuous semigroups of operators on any Banach space $E$. The condition for the hyperbolicity of a semigroup on $E$ is given in terms of the generator of an evolutionary semigroup acting in the…

Dilated Convolutions have been shown to be highly useful for the task of image segmentation. By introducing gaps into convolutional filters, they enable the use of larger receptive fields without increasing the original kernel size. Even…

We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process…

We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…

First, we present some results about the H\"older continuity of the sample paths of so called dilatively stable processes which are certain infinitely divisible processes having a more general scaling property than self-similarity. As a…